-point invariants of real geometries.
Metric characterizations of hyperbolic and Euclidean spaces
Metric properties of the Stephanos bijection.
Minimal paradoxical decomposition for Mycielski's square
Möbius gyrovector spaces in quantum information and computation
Hyperbolic vectors, called gyrovectors, share analogies with vectors in Euclidean geometry. It is emphasized that the Bloch vector of Quantum Information and Computation (QIC) is, in fact, a gyrovector related to Möbius addition rather than a vector. The decomplexification of Möbius addition in the complex open unit disc of a complex plane into an equivalent real Möbius addition in the open unit ball of a Euclidean 2-space is presented. This decomplexification proves useful, enabling the resulting...
Möbius metric in sector domains
The Möbius metric is studied in the cases, where its domain is an open sector of the complex plane. We introduce upper and lower bounds for this metric in terms of the hyperbolic metric and the angle of the sector, and then use these results to find bounds for the distortion of the Möbius metric under quasiregular mappings defined in sector domains. Furthermore, we numerically study the Möbius metric and its connection to the hyperbolic metric in polygon domains.
Mutation and volumes of knots in S3.